Involve: A Journal of Mathematics

  • Involve
  • Volume 12, Number 4 (2019), 607-631.

Irreducible character restrictions to maximal subgroups of low-rank classical groups of types $B$ and $C$

Kempton Albee, Mike Barnes, Aaron Parker, Eric Roon, and A. A. Schaeffer Fry

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Abstract

Representations are special functions on groups that give us a way to study abstract groups using matrices, which are often easier to understand. In particular, we are often interested in irreducible representations, which can be thought of as the building blocks of all representations. Much of the information about these representations can then be understood by instead looking at the trace of the matrices, which we call the character of the representation. This paper will address restricting characters to subgroups by shrinking the domain of the original representation to just the subgroup. In particular, we will discuss the problem of determining when such restricted characters remain irreducible for certain low-rank classical groups.

Article information

Source
Involve, Volume 12, Number 4 (2019), 607-631.

Dates
Received: 12 February 2018
Revised: 11 October 2018
Accepted: 12 October 2018
First available in Project Euclid: 30 May 2019

Permanent link to this document
https://projecteuclid.org/euclid.involve/1559181655

Digital Object Identifier
doi:10.2140/involve.2019.12.607

Mathematical Reviews number (MathSciNet)
MR3941601

Zentralblatt MATH identifier
07072542

Subjects
Primary: 20C15: Ordinary representations and characters 20C33: Representations of finite groups of Lie type

Keywords
irreducible characters classical groups

Citation

Albee, Kempton; Barnes, Mike; Parker, Aaron; Roon, Eric; Schaeffer Fry, A. A. Irreducible character restrictions to maximal subgroups of low-rank classical groups of types $B$ and $C$. Involve 12 (2019), no. 4, 607--631. doi:10.2140/involve.2019.12.607. https://projecteuclid.org/euclid.involve/1559181655


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